4y=2/3(6y)

Solution for 4y=2/3(6y) equation:

4y=2/3(6y)

We move all terms to the left:

4y-(2/3(6y))=0


Domain of the equation: 36y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

4y-(+2/36y)=0

We get rid of parentheses

4y-2/36y=0

We multiply all the terms by the denominator


4y*36y-2=0

Wy multiply elements

144y^2-2=0

a = 144; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·144·(-2)
Δ = 1152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*144}=\frac{0-24\sqrt{2}}{288}
=-\frac{24\sqrt{2}}{288}
=-\frac{\sqrt{2}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*144}=\frac{0+24\sqrt{2}}{288}
=\frac{24\sqrt{2}}{288}
=\frac{\sqrt{2}}{12}
$